The Role of Information in Managing Interactions from a Multifractal Perspective

In the framework of the multifractal hydrodynamic model, the correlations informational entropy–cross-entropy manages attractive and repulsive interactions through a multifractal specific potential. The classical dynamics associated with them imply Hubble-type effects, Galilei-type effects, and dependences of interaction constants with multifractal degrees at various scale resolutions, while the insertion of the relativistic amendments in the same dynamics imply multifractal transformations of a generalized Lorentz-type, multifractal metrics invariant to these transformations, and an estimation of the dimension of the multifractal Universe. In such a context, some correspondences with standard cosmologies are analyzed. Since the same types of interactions can also be obtained as harmonics mapping between the usual space and the hyperbolic plane, two measures with uniform and non-uniform temporal flows become functional, temporal measures analogous with Milne’s temporal measures in a more general manner. This work furthers the analysis published recently by our group in “Towards Interactions through Information in a Multifractal Paradigm”.     

On completeness of eigenfunctions of the one-speed transport equation

It is shown that the set of Case's eigenfunctions of the one speed transport equation is complete in the rigged Hilbert spaceW ₂ ¹ ([?1, 1])?L ₂(?1, 1)?W ₂ ^?1 ([?1, 1]).     

Iron-catalyzed enyne cross-coupling reaction

In the presence of 0.5-1 mol % of FeCl(3) with lithium bromide as a crucial additive, alkynyl Grignard reagents, prepared from the corresponding alkynes and methylmagnesium bromide, react with alkenyl bromides or triflates to give the corresponding conjugated enynes in high to excellent yields. The reaction shows wide applicability to various terminal alkynes and alkenyl electrophiles.     

tert‐Amino effect at a coumarin and a 2‐quinolone system: Synthesis of 1,2 fused 5H‐chromeno[4,3‐b]pyridin‐5‐ones and a 6H‐benzo[h][1,6]naphthyridin‐5‐one

Some novel 1,2‐fused 5H‐chromeno[4,3‐b]pyridin‐5‐ones ( 5a,b ) and a 6H‐benzo[h][1,6]naphthyridin‐5‐one ( 5c ) have been synthesized starting from the 4‐chlorocoumarin‐3‐carbaldehyde ( 1a ) or its N‐methyl‐2‐quinolone analogue ( 1b ) via subsequent Knoevenagel condensation and ring closure reaction known as the ‘tert‐amino effect’. These are rare examples of the tert‐amino effect occurring at 2‐pyrone and 2‐pyridone ring. An unusual intramolecular redox reaction of the iminium ion 6 , reported earlier, most probably follows analogous mechanism as the tert‐amino effect reactions leading to 5 .     

Fluorescent tetraruthenated porphyrins embedded in monolithic SiO2 gels by the sol-gel process

In this work silica gels have been prepared by a sol-gel method using tetraethylorthosilicate as gel precursor. The tetraruthenated porphyrins H2(3-TRPyP), Co(3-TRPyP), and H2(4-TRPyP) were incorporated into the systems during gel formation without problems commonly found in the process, such as aggregation. Spectroscopic studies of the resulting silica gels revealed the presence of absorption bands in the range 200-400 nm associated with the transitions of the groups ruthenium-bipyridine, along with the Soret band at the same wavelengths observed in solution. The porphyrins were found to preserve fluorescence emission properties in the range 650-700 nm even after the aging period. Study of the thermal behavior and decomposition kinetics evidenced that the porphyrin H2(4-TRPyP) is the least stable of the group and that all compounds decompose according to first-order kinetics.     

4,2-Ribbon like ferromagnetic cyano-bridged Fe(III)2Ni(II) chains: a magneto-structural study

The low-spin iron(III) complex AsPh(4)[Fe(III)(bpy)(CN)(4)].CH(3)CN (1) [AsPh(4) = tetraphenylarsonium cation] and the heterobimetallic chains [{Fe(III)(L)(CN)(4)}(2)Ni(II)(H(2)O)(2)].4H(2)O with L = bpy (2) and phen (3) [bpy = 2,2'-bipyridine and phen = 1,10-phenanthroline] have been prepared and their structures determined by X-ray diffraction methods. The structure of 1 consists of mononuclear [Fe(bpy)(CN)(4)](-) anions, tetraphenylarsonium cations and acetonitrile molecules of crystallization. The iron(III) is hexacoordinated with two nitrogen atoms of the bidentate bpy and four carbon atoms of four terminal cyanide groups building a distorted octahedral surrounding around the metal atom. 2 and 3 are isomorphous compounds whose structure is made up of neutral 4,2-ribbon like bimetallic chains of formula [{Fe(III)(L)(CN)(4)}(2)Ni(II)(H(2)O)(2)] where the [Fe(III)(L)(CN)(4)](-) unit acts as a bis-monodentate bridging ligand toward the trans-diaquanickel(II) units through two of its four cyanide groups in cis positions. The chains exhibit two orientations in the unit cell and they interact with each other through hydrogen bonds involving the coordination and crystallization water molecules together with the uncoordinated cyanide nitrogen atoms of the [Fe(L)(CN)(4)](-) units. Compounds 2 and 3 behave as ferromagnetic Fe(III)(2)Ni(II) chains which interact ferromagnetically at very low temperatures in the case of 2, whereas metamagnetic-like behaviour is observed for with a critical field (H(c)) around 200 G. For H > H(c) the ferromagnetic Fe(III)(2)Ni(II) chains of 3 exhibit a frequency dependence of the out-of-phase ac susceptibility signal at T < 3.5 K.     

Estimation of the Refractive Index Change in Glass Induced by Femtosecond Laser Pulses

It is known that local refractive index change occurs when femtosecond laser pulses with extremely high peak power are launched into glass. We focused 130-femtosecond laser pulses of 800 nm into the bulk of glass and examined the shape of the induced refractive index change. We found that the length of the spot of the refractive index change along the optical axis reached about 30 μm despite the diameter being about 2 μm. To estimate the distribution of induced refractive index change, we fabricated Bragg grating by scanning the focused spot and calculated the amount of the change by applying Kogelnik’s coupled mode theory to the measured diffraction efficiencies of the higher order diffracted beams.     

The enhancement and scale up of the extraction of anti-oxidants from Rosmarinus officinalis using ultrasound

The aim of this study was to examine the effect of ultrasound on the solvent extraction of anti-oxidants from the rosemary herb and to scale up the ultrasonic extraction process. The anti-oxidants of interest were identified using HPLC. Results indicated that, compared with conventional solvent extraction, the use of ultrasound gives a more effective extraction at lower temperatures with less dependence on the extraction solvent employed and that scale up of the process is possible.